Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

Diversity and linkage disequilibrium in farmed Tasmanian Atlantic salmon

Farmed Atlantic salmon (Salmo salar) is a globally important production species, including in Australia where breeding and selection has been in progress since the 1960s. The recent development of SNP genotyping platforms means genome‐wide association and genomic prediction can now be implemented to speed genetic gain. As a precursor, this study collected genotypes at 218 132 SNPs in 777 fish from a Tasmanian breeding population to assess levels of genetic diversity, the strength of linkage disequilibrium (LD) and imputation accuracy. Genetic diversity in Tasmanian Atlantic salmon was lower than observed within European populations when compared using four diversity metrics. The distribution of allele frequencies also showed a clear difference, with the Tasmanian animals carrying an excess of low minor allele frequency variants. The strength of observed LD was high at short distances (<25 kb) and remained above background for marker pairs separated by large chromosomal distances (hundreds of kb), in sharp contrast to the European Atlantic salmon tested. Genotypes were used to evaluate the accuracy of imputation from low density (0.5 to 5 K) up to increased density SNP sets (78 K). This revealed high imputation accuracies (0.89–0.97), suggesting that the use of low density SNP sets will be a successful approach for genomic prediction in this population. The long‐range LD, comparatively low genetic diversity and high imputation accuracy in Tasmanian salmon is consistent with known aspects of their population history, which involved a small founding population and an absence of subsequent introgression. The findings of this study represent an important first step towards the design of methods to apply genomics in this economically important population.     

Measuring the extent of linkage disequilibrium in commercial pig populations

To evaluate the extent of linkage disequilibrium in domestic pigs, we genotyped 33 and 44 unrelated individuals from two commercial populations for 29 and five microsatellite markers located on chromosomes 15 and 2 respectively. A high proportion of marker pairs up to 40 cM apart exhibited significant linkage disequilibrium in both populations. Pair-wise r(2) values averaged between 0.15 and 0.50 (depending on chromosome and population) for markers <1 cM apart and declined to values of 0.05 for more distant syntenic markers. Our results suggest that both populations underwent a bottleneck approximately 20 generations ago, which reduced the effective population size from thousands to <200 animals.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Detection of QTL affecting harvest traits in a commercial Atlantic salmon population

Genetic variation in performance and quality traits measured at harvest has previously been demonstrated in Atlantic salmon aquaculture populations. To map major loci underlying this variation, we utilized data from 10 families from a commercial breeding programme. Significant QTL were detected affecting harvest weight and length traits on linkage group 1, and affecting waste weight on linkage group 5. In total, 11 of the 29 linkage groups examined showed at least suggestive evidence for a QTL. These data suggest that major loci affecting economically important harvest characteristics are segregating in commercial salmon populations.     

Markers for mapping by admixture linkage disequilibrium in African American and Hispanic populations

Population linkage disequilibrium occurs as a consequence of mutation, selection, genetic drift, and population substructure produced by admixture of genetically distinct ethnic populations. African American and Hispanic ethnic groups have a history of significant gene flow among parent groups, which can be of value in affecting genome scans for disease-gene discovery in the case-control and transmission/disequilibrium test designs. Disease-gene discovery using mapping by admixture linkage disequilibrium (MALD) requires a map of polymorphic markers that differentiate between the founding populations, along with differences in disease-gene allele frequencies. We describe markers appropriate for MALD mapping by assessing allele frequencies of 744 short tandem repeats (STRs) in African Americans, Hispanics, European Americans, and Asians, by choosing STR markers that have large differences in composite delta, log-likelihood ratios, and/or I*(2) for MALD. Additional markers can be added to this MALD map by utilization of the rapidly growing single-nucleotide-polymorphism databases and the literature, to achieve a 3-10-cM scanning scale. The map will be useful for studies of diseases, including prostate and breast cancer, diabetes, hypertension, and end-stage renal disease, that have large differences in incidence between the founding populations of either Hispanics or African Americans.     

Extent and consistency across generations of linkage disequilibrium in commercial layer chicken breeding populations

Recent studies report a surprisingly high degree of marker-to-marker linkage disequilibrium (LD) in ruminant livestock populations. This has important implications for QTL mapping and marker-assisted selection. This study evaluated LD between microsatellite markers in a number of breeding populations of layer chickens using the standardized chi-square (chi(2')) measure. The results show appreciable LD among markers separated by up to 5 cM, decreasing rapidly with increased separation between markers. The LD within 5 cM was strongly conserved across generations and differed among chromosomal regions. Using marker-to-marker LD as an indication for marker-QTL LD, a genome scan of markers spaced 2 cM apart at moderate power would have good chances of uncovering most QTL segregating in these populations. However, of markers showing significant trait associations, only 57% are expected to be within 5 cM of the responsible QTL, and the remainder will be up to 20 cM away. Thus, high-resolution LD mapping of QTL will require dense marker genotyping across the region of interest to allow for interval mapping of the QTL.     

A comparison of linkage disequilibrium patterns and estimated population recombination rates across multiple populations

Large-scale studies of linkage disequilibrium (LD) have shown considerable variation in the extent and distribution of pairwise LD within and between populations. Taken at face value, these results suggest that genomewide LD maps for one population may not be generalizable to other populations. However, at least part of this diversity is due to some undesirable features of pairwise LD measures, which are well documented for the D' and r2 measures. In this report, we compare patterns of LD derived from pairwise measures with statistical estimates of population recombination rates ( rho ) along a 10-Mb stretch of chromosome 20 in four population samples, comprising East Asians, African Americans, and U.K. and U.S. individuals of western European descent. The results reveal the expected variability of D' within and between populations but show better concordance in estimates of r2 for the same markers across the population samples. Estimates of rho correlate well across populations, but there is still evidence of population-specific spikes and troughs in rho values. We conclude that it is unlikely that a single haplotype map will provide a definitive guide for association studies of many populations; rather, multiple maps will need to be constructed to provide the best-possible guides for gene mapping.     

Assessing footprints of selection in commercial Atlantic salmon populations using microsatellite data

Relatively large rates of response to traits of economic importance have been observed in different selection experiments in salmon. Several QTL have been mapped in the salmon genome, explaining unprecedented levels of phenotypic variation. Owing to the relatively large selection intensity, individual loci may be indirectly selected, leaving molecular footprints of selection, together with increased inbreeding, as its likely relatives will share the selected loci. We used population differentiation and levels of linkage disequilibrium in chromosomes known to be harbouring QTL for body weight, infectious pancreatic necrosis resistance and infectious salmon anaemia resistance to assess the recent selection history at the genomic level in Atlantic salmon. The results clearly suggest that the marker SSA0343BSFU on chromosome 3 (body weight QTL) showed strong evidence of directional selection. It is intriguing that this marker is physically mapped to a region near the coding sequence of DVL2 , making it an ideal candidate gene to explain the rapid evolutionary response of this chromosome to selection for growth in Salmo salar. Weak evidence of diversifying selection was observed in the QTL associated with infectious pancreatic necrosis and infectious salmon anaemia resistance. Overall, this study showed that artificial selection has produced important changes in the Atlantic salmon genome, validating QTL in commercial salmon populations used for production purposes according to the recent selection history.     

Optimal designs for linkage disequilibrium mapping and candidate gene association tests in livestock populations

Simulation was used to evaluate the performance of different selective genotyping strategies when using linkage disequilibrium across large half-sib families to position a QTL within a previously defined genomic region. Strategies examined included standard selective genotyping and different approaches of discordant and concordant sib selection applied to arbitrary or selected families. Strategies were compared as a function of effect and frequency of QTL alleles, heritability, and phenotypic expression of the trait. Large half-sib families were simulated for 100 generations and 2% of the population was genotyped in the final generation. Simple ANOVA was applied and the marker with the greatest F-value was considered the most likely QTL position. For traits with continuous phenotypes, genotyping the most divergent pairs of half-sibs from all families was the best strategy in general, but standard selective genotyping was somewhat more precise when heritability was low. When the phenotype was distributed in ordered categories, discordant sib selection was the optimal approach for positioning QTL for traits with high heritability and concordant sib selection was the best approach when genetic effects were small. Genotyping of a few selected sibs from many families was generally more efficient than genotyping many individuals from a few highly selected sires.     

QTL fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium at a series of linked marker loci in extreme samples of populations

It has recently been demonstrated that fine-scale mapping of a susceptibility locus for a complex disease can be accomplished on the basis of deviations from Hardy-Weinberg (HW) equilibrium at closely linked marker loci among affected individuals. We extend this theory to fine-scale localization of a quantitative-trait locus (QTL) from extreme individuals in populations, by means of HW and linkage-disequilibrium (LD) analyses. QTL mapping and/or linkage analyses can establish a large genomic region ( approximately 30 cM) that contains a QTL. The QTL can be fine mapped by examination of the degree of deviation from HW and LD at a series of closely linked marker loci. The tests can be performed for samples of individuals belonging to either high or low percentiles of the phenotype distribution or for combined samples of these extreme individuals. The statistical properties (the power and the size) of the tests of this fine-mapping approach are investigated and are compared extensively, under various genetic models and parameters for the QTL and marker loci. On the basis of the results, a two-stage procedure that uses extreme samples and different tests (for HW and LD) is suggested for QTL fine mapping. This two-step procedure is economic and powerful and can accurately narrow a genomic region containing a QTL from approximately 30-1 cM, a range that renders physical mapping feasible for identification of the QTL. In addition, the relationship between parameterizations of complex diseases, by means of penetrance, and those of complex quantitative traits, by means of genotypic values, is outlined. This means that many statistical genetic methods developed for searching for susceptibility loci of complex diseases can be directly adopted and/or extended to QTL mapping for quantitative traits.     

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL

Effectiveness of marker-assisted selection (MAS) and quantitative trait loci (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTL depends on the extent of LD and how it declines with distance in a population. Because marker-QTL LD cannot be observed directly, the objective of this study was to evaluate alternative measures of observable LD between multi-allelic markers as predictors of usable LD of multi-allelic markers with presumed biallelic QTL. Observable LD between marker pairs was evaluated using eight existing measures and one new measure. These consisted of two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy-Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. In simulated populations with a range of LD generated by drift and a range of marker polymorphism, marker-marker LD measured by a standardized chi-square statistic (denoted chi(2')) was found to be the best predictor of useable marker-QTL LD for a group of multi-allelic markers. Estimates of the level and decline of marker-marker LD with distance obtained from chi(2') were linearly and highly correlated with usable LD of those markers with QTL across population structures and marker polymorphism. Corresponding relationships were poorer for the other marker-marker LD measures. Therefore, when LD is generated by drift, chi(2') is recommended to quantify the amount and extent of usable LD in a population for QTL mapping and MAS based on multi-allelic markers.     

Demography,recombination hotspot intensity,and the block structure of linkage disequilibrium

BACKGROUND: Effective gene mapping based on genetic association data will require detailed knowledge of patterns of linkage disequilibrium (LD) in human populations. It has been recently suggested that linkage disequilibrium in humans may be organized in a block-like structure, with islands of high LD separated by regions of rapid breakdown of LD due to recombination hotspots. The experimental data to date, however, are limited, and fundamental questions remain about the implications of recombination rate heterogeneity. Here, we use computer simulations to evaluate how such heterogeneity influences patterns of LD, and we develop formal criteria to assess whether the patterns are functionally block like in the context of association mapping.RESULTS: Our analyses suggest that, even in models of extreme recombination rate heterogeneity, some human populations will have a functionally block-like structure to the pattern of LD, but others will not, depending on their precise demographic histories. In fact, for many models, we find that, following an LD-generating event, populations may move through discrete phases that can be functionally described as pre-block, block, and post-block. An analysis of observed and expected patterns of LD surrounding hotspots within the MHC Class II region confirms these theoretical expectations.CONCLUSIONS: Even if highly punctuated patterns of recombination are the rule, patterns of LD are still likely to show differences among populations and among genomic regions that are of practical importance in the design of genetic association studies. The notion that the average extent of LD is a useful concept for the design of association studies must be abandoned in light of the experimental and theoretical evidence.     

The effects of genotype-dependent recombination, and transmission asymmetry, on linkage disequilibrium

A recent sperm-typing study by Jeffreys and Neumann suggested that recombination rates in different individuals at the DNA2 recombination hotspot appeared to be highly dependent on their genotype at a particular A/G SNP, FG11. Specifically, individuals who carried at least one copy of the A allele at this SNP exhibited rates of crossover considerably higher than those of individuals with no copies. Further, recombinant sperm from heterozygous individuals showed a preferential tendency to carry the G allele. We consider the effects of these phenomena on patterns of linkage disequilibrium and find them to be more subtle than might have been expected. In particular, our analysis suggests that, perhaps surprisingly, patterns of LD among chromosomes carrying the "hot" allele (in this case, A) will typically be similar to those among chromosomes carrying the "cold" allele (G).     

Power and precision of alternate methods for linkage disequilibrium mapping of quantitative trait loci

Linkage disequilibrium (LD) analysis in outbred populations uses historical recombinations to detect and fine map quantitative trait loci (QTL). Our objective was to evaluate the effect of various factors on power and precision of QTL detection and to compare LD mapping methods on the basis of regression and identity by descent (IBD) in populations of limited effective population size (N(e)). An 11-cM region with 6-38 segregating single-nucleotide polymorphisms (SNPs) and a central QTL was simulated. After 100 generations of random mating with N(e) of 50, 100, or 200, SNP genotypes and phenotypes were generated on 200, 500, or 1000 individuals with the QTL explaining 2 or 5% of phenotypic variance. To detect and map the QTL, phenotypes were regressed on genotypes or (assumed known) haplotypes, in comparison with the IBD method. Power and precision to detect QTL increased with sample size, marker density, and QTL effect. Power decreased with N(e), but precision was affected little by N(e). Single-marker regression had similar or greater power and precision than other regression models, and was comparable to the IBD method. Thus, for rapid initial screening of samples of adequate size in populations in which drift is the primary force that has created LD, QTL can be detected and mapped by regression on SNP genotypes without recovering haplotypes.     

Insights into recombination from patterns of linkage disequilibrium in humans

An ability to predict levels of linkage disequilibrium (LD) between linked markers would facilitate the design of association studies and help to distinguish between evolutionary models. Unfortunately, levels of LD depend crucially on the rate of recombination, a parameter that is difficult to measure. In humans, rates of genetic exchange between markers megabases apart can be estimated from a comparison of genetic and physical maps; these large-scale estimates can then be interpolated to predict LD at smaller ("local") scales. However, if there is extensive small-scale heterogeneity, as has been recently proposed, local rates of recombination could differ substantially from those averaged over much larger distances. We test this hypothesis by estimating local recombination rates indirectly from patterns of LD in 84 genomic regions surveyed by the SeattleSNPs project in a sample of individuals of European descent and of African-Americans. We find that LD-based estimates are significantly positively correlated with map-based estimates. This implies that large-scale, average rates are informative about local rates of recombination. Conversely, although LD-based estimates are based on a number of simplifying assumptions, it appears that they capture considerable information about the underlying recombination rate or at least about the ordering of regions by recombination rate. Using LD-based estimators, we also find evidence for homologous gene conversion in patterns of polymorphism. However, as we demonstrate by simulation, inferences about gene conversion are unreliable, even with extensive data from homogeneous regions of the genome, and are confounded by genotyping error.     

Combining sperm typing and linkage disequilibrium analyses reveals differences in selective pressures or recombination rates across human populations

A previous polymorphism survey of the type 2 diabetes gene CAPN10 identified a segment showing an excess of polymorphism levels in all population samples, coinciding with localized breakdown of linkage disequilibrium (LD) in a sample of Hausa from Cameroon, but not in non-African samples. This raised the possibility that a recombination hotspot is present in all populations and we had insufficient power to detect it in the non-African data. To test this possibility, we estimated the crossover rate by sperm typing in five non-African men; these estimates were consistent with the LD decay in the non-African, but not in the Hausa data. Moreover, resequencing the orthologous region in a sample of Western chimpanzees did not show either an excess of polymorphism level or rapid LD decay, suggesting that the processes underlying the patterns observed in humans operated only on the human lineage. These results suggest that a hotspot of recombination has recently arisen in humans and has reached higher frequency in the Hausa than in non-Africans, or that there is no elevation in crossover rate in any human population, and the observed variation results from long-standing balancing selection.     

Extent and genome-wide distribution of linkage disequilibrium in commercial maize germplasm

Association mapping is based on linkage disequilibrium (LD) resulting from historical recombinations and helps understanding the genetic basis of complex traits. Many factors affect LD and, therefore, it must be determined empirically in the germplasm under investigation to examine the prospects of successful genome-wide association mapping. The objectives of our study were to (1) examine the extent of LD with simple sequence repeat (SSR) and single nucleotide polymorphism (SNP) markers in 1,537 commercial maize inbred lines belonging to four heterotic pools, (2) compare the LD patterns determined by these two marker types, (3) evaluate the number of SNP markers needed to perform genome-wide association analyses, and (4) investigate temporal trends of LD. Mean values of the squared correlation coefficient ( $ \bar{R} $ ) were almost identical for unlinked, linked, and adjacent SSR marker pairs. In contrast, $ \bar{R} $ values were lowest for the unlinked SNP loci and highest for the SNPs within amplicons. LD decay varied across the different heterotic pools and the individual chromosomes. The SSR markers employed in the present study are not adequate for association analysis, because of insufficient marker density for the germplasm evaluated. Based on the decay of LD in the various heterotic pools, we would need between 4,000 and 65,000 SNP markers to detect with a reasonable power associations with rather large quantitative trait loci (QTL). A much higher marker density is required to identify QTL with smaller effects. However, not only the total number of markers but also their distribution among and along the chromosomes are primordial for undertaking powerful association analyses.     

Temporal dynamics and linkage disequilibrium in natural Caenorhabditis elegans populations

Caenorhabditis elegans is a major laboratory model system yet a newcomer to the field of population genetics, and relatively little is known of its biology in the wild. Recent studies of natural populations at a single time point revealed strong spatial population structure and suggested that these populations may be very dynamic. We have therefore studied several natural C. elegans populations over time and genotyped them at polymorphic microsatellite loci. While some populations appear to be genetically stable over the course of observation, others seem to go extinct, with full replacement of multilocus genotypes upon regrowth. The frequency of heterozygotes indicates that outcrossing occurs at a mean frequency of 1.7% and is variable between populations. However, in genetically stable populations, linkage disequilibrium between different chromosomes can be maintained over several years at a level much higher than expected from the heterozygote frequency. C. elegans seems to follow metapopulation dynamics, and the maintenance of linkage disequilibrium despite a low yet significant level of outcrossing suggests that selection may act against the progeny of outcrossings.